Synchronisation and dynamics of model cilia and flagella

Cilia and flagella are organelles central to fluid transport around tissues, unicellular locomotion, and in early mammalian development. They are observed to undulate, rotate, and beat symmetrically in pairs or even in large numbers via metachronal waves. Inspired by biflagellate swimmers like Chlamydomonas, we analyse the synchronisation and dynamics exhibited by pairs of filaments in a Stokesian flow regime. Using a fully three-dimensional filament model, we study the regions of bistable synchrony exhibited by two filaments tethered to a wall beating via a base-driven, geometric switch model. We establish the existence of two stable and two unstable branches of synchrony, characterising the unstable anti-phase branch using Floquet analysis and characterising the unstable edge state between two basins of attraction via a bisection algorithm and the tracking of the edge behaviour in time. We fully characterise a bifurcation diagram, the nature of the bifurcation points, and model the observed dynamical system with a modified Adler equation. We also find that the two-filament model prefers anti-phase synchrony upon the introduction of small basal-body coupling and a preferred curvature. We further study the effectiveness of oscillator systems in capturing two-filament synchronisation and develop a novel minimum-model which encapsulates the qualitative synchronisation behaviours exhibited in elastic filament dynamics by introducing wall effects to the oscillator system. Finally, extending the base-driven filament model to two filament pairs (four filaments), of varying pairwise separation distances, we study the dynamical behaviours along ciliary rows and between flagellate somatic cells as in the case of microalgae like Gonium or Volvox. We quantify different synchronisation states exhibited by four types of pairs and find that different synchronisation states can coexist simultaneously (a form of bistability). We further characterise the bistable region and its transitions regarding disorder in the dynamical system.Open Acces